Unbounded Lebesgue constants on compact groups |
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Authors: | Christopher Meaney |
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Institution: | (1) Department of Mathematics, University of Otago, P. O. Box 56, Dunedin, New Zealand;(2) School of Mathematics, University of NSW, 2033 Kensington, NSW, Australia |
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Abstract: | LetG be a compact group with dual object . A decomposition of into pairwise disjoint finite sets provides a way of defining partial sums of Fourier series onG. We employ a theorem of Olevskii to present a condition on such a decomposition which, if satisfied, guarantees that the corresponding Lebesgue constants are unbounded. We apply this to certain summation methods on tori and compact connected semisimple Lie groups. |
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